A360170 a(n) is the X-coordinate after n steps of an infinite knight's tour through all lattice points; see A360171 for the Y-coordinates.

0, 1, -1, -2, 0, 2, 1, -1, -2, -1, 1, 2, 0, -2, -1, 1, 2, 0, -2, -1, -2, 0, 2, 1, 2, 3, 1, -1, -3, -4, -3, -4, -2, 0, 2, 4, 3, 4, 3, 1, -1, -3, -4, -3, -4, -3, -1, 1, 3, 4, 3, 4, 2, 0, -2, -4, -3, -4, -3, -1, 1, 3, 4, 3, 4, 2, 0, -2, -4, -3, -4, -3, -4, -2, 0

Offset: 0

Author

Rémy Sigrist, Jan 28 2023

Keywords

• sign

Comments

See A068608 for similar sequences.

Examples

			See illustration of the first steps in Links section.
		

Links

• Robert Bosch and Zejian Huang, Structured Knight’s Tours
• Mathematics StackExchange, Infinite Knight's Tour
• Rémy Sigrist, Illustration of the first steps (where colors denote the direction to the next position)
• Rémy Sigrist, PARI program
• Dan Thomasson, Knight's Tour Art
• Wikipedia, Knight's tour
• Wolfram Demonstrations Project, An Infinite Knight's Tour
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

Cf. A068608, A068613, A174344, A360171.

Programs

PARI

See Links section.

Formula

a(n) = A174344(A068613(n+1)).